Math 30-1 Help, Built for Alberta's Curriculum

Math 30-1 curriculum: 7 units, 51 lessons (Alberta Mathematics 30-1)

Unit 1: Function Transformations & Operations

Translations, reflections and stretches, inverses, and operations and composition of functions.

• Function Foundations, Refresh function notation, domain and range, and how to evaluate f(x), the groundwork every Math 30-1 unit builds on.
• Piecewise Functions, Graph functions defined by different rules on different intervals, and evaluate them by picking the right piece for each x-value.
• Sums & Difference of Functions, Build h(x) = f(x) + g(x) or f(x) - g(x), sketch the combined graph, and state the domain the two functions share.
• Products & Quotients of Functions, Multiply and divide functions, then pin down the new domain, especially where a quotient's denominator hits zero.
• Composite Functions, Evaluate and simplify compositions like f(g(x)) by working from the inside out, a skill the diploma exam leans on heavily.
• Horizontal & Vertical Translations, Slide graphs left, right, up or down with y - k = f(x - h), and write the equation of a shifted graph from its picture.
• Reflections & Stretches, Reflect graphs in the x-axis or y-axis and stretch them by a factor, predicting which points move and which stay fixed.
• Combining Transformations, Apply stretches, reflections and translations in the right order to sketch y = af(b(x - h)) + k from a base graph.
• Inverse Functions, Swap x and y to find an inverse algebraically, sketch its reflection in the line y = x, and restrict a domain so the inverse is a function.

Unit 2: Polynomial Functions

Characteristics of polynomials, dividing them, the factor theorem, graphing, and polynomial equations and inequalities.

• Characteristics of Polynomial Functions, Read degree and leading coefficient to predict end behaviour and the possible numbers of x-intercepts and turning points.
• Dividing Polynomials, Divide polynomials using long and synthetic division, and connect each remainder to the remainder theorem.
• Factoring & the Factor Theorem, Test whether x - a is a factor by checking if P(a) = 0, then combine the factor theorem with division to factor cubics and quartics.
• Graphing Polynomial Functions, Sketch cubics, quartics and quintics from factored form, using intercepts, multiplicity and end behaviour as your guide.
• Polynomial Equations & Inequalities, Solve polynomial equations by factoring, then use a sign analysis or the graph to handle inequalities like P(x) > 0.
• Solving Problems with Polynomial Functions, Model volume, area and other quantities with polynomials, then solve for the dimensions that meet a given condition.

Unit 3: Exponents & Logarithms

Exponential and logarithmic functions, the log laws, and solving exponential and log equations.

• Exponential Functions & Their Equations
• Transformations of Exponential Functions
• Solving Exponential Equations, Solve equations like 3^(2x) = 7 by matching bases when possible and taking a logarithm of both sides when not.
• Applications of Exponential Functions
• Understanding Logarithms
• Logarithmic Functions & Their Equations
• Laws of Logarithms, Expand and condense log expressions using the product, quotient and power laws, the algebra behind solving log equations.
• Solving Equations with Logarithms
• Applications of Logarithms

Unit 4: Trigonometric Ratios & Functions

Angles and the unit circle, the trig ratios, solving trigonometric equations, and graphing and transforming the trig functions.

• Angle Foundations
• The Unit Circle, The unit circle links angles to coordinates, memorize special angles like π/6 and π/4 and read exact trig values straight off the circle.
• Trigonometric Ratios
• Solving Trigonometric Equations (Linear)
• Solving Trigonometric Equations (Quadratic)
• Graphing Trigonometric Functions
• Transformations
• Tangent Functions
• Applications

Unit 5: Trigonometric Identities

Reciprocal, Pythagorean, sum and difference, and double angle identities, and proving them.

• Reciprocal & Quotient Identities, Turn tangent into sine over cosine and secant into one over cosine, applying quotient and reciprocal identities to simplify.
• Pythagorean Identities, Work with sin²x + cos²x = 1 and its rearrangements to simplify expressions and trade one trig ratio for another.
• Sum & Difference Identities, Break angles apart with formulas like sin(A + B) to find exact values for angles such as 15° that sit off the unit circle.
• Double Angle Identities, Apply sin 2x = 2 sin x cos x and the three forms of cos 2x to collapse expressions that mix single and double angles.
• Tangent Identities
• Proving Trigonometric Identities, Prove identities by working each side independently, pick a side, convert to sines and cosines, and simplify until both match.
• Solving Trigonometric Equations, Solve trig equations exactly over the interval from 0 to 2π, then write general solutions that capture every rotation.

Unit 6: Radical & Rational Functions

Radical and rational functions, asymptotes, and solving radical and rational equations.

• Solving Radical Equations, Square both sides to clear a radical, then test every answer, squaring can create extraneous roots that fail the original equation.
• Transformations Of Radical Equations
• Square Root Of Linear Functions
• Square Root Of Quadratic Functions & General Function
• Transformations Of Rational Functions
• Analysing Rational Functions
• Solving Rational Equations

Unit 7: Permutations & Combinations

The counting principle, permutations, combinations, and the binomial theorem.

• Fundamental Counting Principle
• Permutations, Arrange objects where order matters, compute nPr for lineups and codes, including arrangements of words with repeated letters.
• Combinations, Choose groups where order does not matter, evaluate nCr for committees and hands, and see why it divides out the repeated orderings.
• The Binomial Theorem

Frequently asked questions

How hard is Math 30-1?

For most students it is Alberta's toughest high school math course: it moves quickly through pre-calculus topics and ends in a diploma exam. It is entirely manageable with steady work, keep up unit by unit, practice exam-style questions, and get help the moment something stops making sense rather than the week before the exam.

Does this cover the Math 30-1 diploma exam?

Yes. The diploma exam samples the full course, all seven units, in machine-scored multiple choice and numerical response format, and counts for 30% of your final Math 30-1 mark. Studyio pairs every unit with diploma-style practice questions and step-by-step solutions so the format holds no surprises.

What units are in Math 30-1?

Seven units: Function Transformations, Polynomial Functions, Exponents & Logarithms, Trigonometric Functions, Trigonometric Identities, Radical & Rational Functions, and Permutations & Combinations. On Studyio that's 50 lessons, each with a voice-over walkthrough, worked examples, and a practice quiz with full solutions.

Can I use this to upgrade Math 30-1?

Many people rewriting Math 30-1 as adults use Studyio to relearn the course at their own pace before and during an upgrading program. Studyio doesn't grant course credit itself, you still enrol through a school board, online school or upgrading provider, but it covers the same seven units and gives you unlimited diploma-style practice.

What's the difference between Math 30-1 and Math 30-2?

Math 30-1 is the pre-calculus route, required for programs that lead into calculus: engineering, computer science, and most science degrees. Math 30-2 satisfies programs that don't need calculus. Check the current admission requirements for the specific programs you're aiming at, because the streams are not interchangeable once offers go out.

Can Studyio plan my studying for a Math 30-1 test?

Yes. Add a unit test or the Diploma exam, its date and the units it covers, and pick the days you can study. Studyio builds a study plan, a day by day list of the Math 30-1 lessons, quizzes and practice tests to do before then, recommends how many minutes a day will finish everything with a few days kept free, and reshuffles on its own if you miss a day. Free accounts can plan one test; Pro plans every test.

Do I need a credit card to start the trial?

Yes, the 7-day trial runs through Stripe and takes a card when you start, but you aren't charged anything unless you stay past the trial, and cancelling takes a couple of clicks. If you'd rather try without a card, the free version needs no payment details.

What's the difference between the free version and the trial?

Free gets you 5 lessons of your choice, 5 quiz attempts, step-by-step solutions, and limited Ms. Emma (AI tutor) access. The 7-day trial is full Pro access: all 50 Math 30-1 lessons, unlimited quizzes and unit tests, unlimited diploma-style practice, and unlimited Ms. Emma.